The only dumb question is the one that didn't get asked when it should have.

What you "own" is the domain "example.com" and that also gives you ownership and control over all subdomains of that domain including www.

www.example.com
mail.example.com
keyword.example.com

... and so on, are all yours if you own example.com.

www.example.com could indeed be a different website from example.com but you'd own them both. It's rare for them to be developed separately, though. It's more common for careless website developers to let both URLs get into circulation when it's really only intended to be one site.

Use one form or the other and try not to mix and match them.

While the www and non www names are technically two different sites it is conventional to point them both to the same location. Typically your hosting service will have this set up as the default.

Its your choice which to use but as buckworks says it is advisable to standardise on one. Personally I think that typing an extra www is a trivial but ultimately wasteful use of time and bandwidth but if you give people a link without the www I can guarantee that at least half will "correct" it.

Make sure you link to only one and set up a canonical 301 redirect for the other.

Look what appears in your browser URL bar, after you type google.com, and hit enter, for example.

set up a canonical 301 redirect for the other.

Assuming of course that the OP's hosting company will support that. Many cut price hosts don't.